Force, Momentum, and Impulse

We know how to calculate the kinetic energy of moving
objects -- isn't that enough? No. It turns out that many
situations involving collisions do not obey the simple
conservation of Mechanical Energy. Why not? Because it takes
energy to bend, break, mutilate and deform objects, energy
which disappears from the kinetic and gravitational potential
energy.

But a different quantity is conserved, even during
collisions. The linear momentum of an object is
defined as

p = (mass) * (velocity)

It is a vector quantity, and the total linear momentum of
a bunch of objects will remain the same, before and after
a collision.

Momentum is connected to force by impulse,
which is simply

impulse = (force) * (time)

if the force has a constant magnitude during its action.
If the force changes with time, then one must integrate
to find the impulse:

/
impulse = | (force) dt
/

The Momentum-Impulse Theorem states that the change in
momentum of an object is equal to the impulse exerted on it: